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ExtremeBDS [4]
3 years ago
13

The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would l

ike to increase statewide highway speed to 75 from 65 mph. At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.07 of the true proportion?
Mathematics
1 answer:
N76 [4]3 years ago
6 0

Answer: 339

Step-by-step explanation:

Since the prior estimate of population proportion is unknown , then we take p= 0.5

Given : Margin of error : E=0.07

Critical value for 99% confidence interval : z_{\alpha/2}=2.576

Formula for sample size :-

n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{2.576}{0.07})^2\\\\=338.56\approx339

Hence, the minimum sample size required = 339

i.e. they need to survey 339 residents.

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